Measure the emergent-photon $T^3$ heat capacity and speed in quantum spin ice

In quantum spin ice the photon speed $c$ is set by the ring-exchange scale $g=12J_{\mathrm{pm}}^{3}/J_{\mathrm{zz}}^{2}$ ($c \sim g$ $a$$/\hbar$ up to a computed prefactor, a the lattice spacing), and the photon heat capacity per volume is $C/V = (4 \pi^{2}/15) k_{\mathrm{B}} (k_{\mathrm{B}} T/\hbar c)^{3}$ for two polarizations. Measure $C/T^{3}$ below the photon bandwidth in a candidate material and compare $c$ with the value from independently fitted exchange parameters. An answer is $c$ measured and predicted, with agreement or disagreement within errors.

Heat capacity below about 0.05 K with nuclear and phonon contributions subtracted, compared with the photon speed from neutron spectra and quantum Monte Carlo.